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Constraints on higher spin CFT2

  • Nima Afkhami-Jeddi
  • Kale Colville
  • Thomas Hartman
  • Alexander Maloney
  • Eric Perlmutter
Open Access
Regular Article - Theoretical Physics

Abstract

We derive constraints on two-dimensional conformal field theories with higher spin symmetry due to unitarity, modular invariance, and causality. We focus on CFTs with \( {\mathcal{W}}_N \) symmetry in the “irrational” regime, where c > N − 1 and the theories have an infinite number of higher-spin primaries. The most powerful constraints come from positivity of the Kac matrix, which (unlike the Virasoro case) is non-trivial even when c > N − 1. This places a lower bound on the dimension of any non-vacuum higher-spin primary state, which is linear in the central charge. At large c, this implies that the dual holographic theories of gravity in AdS3, if they exist, have no local, perturbative degrees of freedom in the semi-classical limit.

Keywords

Higher Spin Symmetry Conformal Field Theory Field Theories in Lower Dimensions Higher Spin Gravity 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Department of PhysicsCornell UniversityIthacaU.S.A.
  2. 2.Department of PhysicsMcGill UniversityMontrealCanada
  3. 3.Department of PhysicsPrinceton UniversityPrincetonU.S.A.

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